Fuzzy Prediction Sets: Conformal Prediction with E-values

2025/09/16 by Nick W. Koning, Koning, Nick W., Sam van Meer +1
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Fuzzy Logic and Control Systems #Machine Learning (stat.ML) #Methodology (stat.ME) #Neural Networks and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2509.13130

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/30

Abstract

Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a fuzzy prediction set is an e-value, capturing precisely what e-values bring to predictive inference. Fuzzy prediction sets inherit the merging properties of their e-value, offer richer guarantees to decision-makers. We also show in what sense optimal e-values give rise to optimal (fuzzy) prediction sets. We apply our results to conformal prediction, deriving optimal fuzzy conformal prediction sets, and characterizing in what sense classical conformal prediction is optimal.

Citations

• A simple geometric proof for the characterisation of e-merging functions
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• There are natural scores: Full comment on Shafer, "Testing by betting: A strategy for statistical and scientific communication"
• False discovery rate control with e-values
• Conformal e-prediction
• Safe Testing
• LEAF: A Benchmark for Federated Settings
• Time-uniform, nonparametric, nonasymptotic confidence sequences
• Learning by Transduction

Related

• Enhancing Conformal Prediction Using E-Test Statistics
• E-Values Expand the Scope of Conformal Prediction
• Robust Yet Efficient Conformal Prediction Sets
• Valid Selection among Conformal Sets
• Conformal e-prediction